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Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample…
Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…
The parallel dynamics of the fully connected Blume-Emery-Griffiths neural network model is studied for arbitrary temperature. By employing a probabilistic signal-to-noise approach, a recursive scheme is found determining the time evolution…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…
Machine learning potentials have achieved great success in accelerating atomistic simulations. Many of them relying on atom-centered local descriptors are natural for parallelization. More recent message passing neural network (MPNN) models…
We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of…
Training neural networks sequentially in time to approximate solution fields of time-dependent partial differential equations can be beneficial for preserving causality and other physics properties; however, the sequential-in-time training…
Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…
The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…
What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained…
We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…
We consider the class of dual-unitary quantum circuits in $1+1$ dimensions and introduce a notion of ``solvable'' matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We…
Sequential neuronal activity underlies a wide range of processes in the brain. Neuroscientific evidence for neuronal sequences has been reported in domains as diverse as perception, motor control, speech, spatial navigation and memory.…
Sequence modeling with neural networks has lead to powerful models of symbolic music data. We address the problem of exploiting these models to reach creative musical goals, by combining with human input. To this end we generalise previous…
When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a…